The Constraint of Causality on an Active Control System

Abstract

This paper discusses a method of ascertaining the optimal performance of a single channel active control system. It looks specifically at the loss of performance introduced by some of the features that are likely to be inherent in real systems. These include the limitations on the control system caused by finite computational power and the need for the controller to be causal. We also consider the effect of noise corruption of the sensor signal and unwanted noise production by the transducer. In order to quantify the effects of these real features on an active control system we first study a perfect system and then observe the effects on the system performance of introducing these features. It is most convenient for clarity in this paper to discuss the simplest active control system; the waveguide.